WASHINGTON — A broad aviation bill that would advance modernization of the nation’s air-traffic control system moved a step closer to passage Thursday. The Senate also rejected a proposal to kill a program that subsidizes air service to small airports, often in remote communities.

The bill would renew Federal Aviation Administration programs for two years, spend $8 billion on new runways and other airport construction projects, and speed up the transition from an air-traffic control system based on World War II-era radar technology to GPS technology.

Florida’s state social services agency investigated Nikolas Cruz’s home life more than a year before police say he killed 17 people at his former high school, closing the inquiry after determining that his “final level of risk is low,” despite learning that the teenager had behavioral struggles and was planning to buy a gun, according to an investigative report.